Question
Answer
$$4y\cdot(5-4y)(2y+6)^2=-64y^4-304y^3-96y^2+720y$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}4y\cdot(5-4y)(2y+6)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}4y\cdot(5-4y)(4y^2+24y+36) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(20y-16y^2)(4y^2+24y+36) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}80y^3+480y^2+720y-64y^4-384y^3-576y^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-64y^4-304y^3-96y^2+720y\end{aligned} $$ | |
| ① | Find $ \left(2y+6\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 2y } $ and $ B = \color{red}{ 6 }$. $$ \begin{aligned}\left(2y+6\right)^2 = \color{blue}{\left( 2y \right)^2} +2 \cdot 2y \cdot 6 + \color{red}{6^2} = 4y^2+24y+36\end{aligned} $$ |
| ② | Multiply $ \color{blue}{4y} $ by $ \left( 5-4y\right) $ $$ \color{blue}{4y} \cdot \left( 5-4y\right) = 20y-16y^2 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{20y-16y^2}\right) $ by each term in $ \left( 4y^2+24y+36\right) $. $$ \left( \color{blue}{20y-16y^2}\right) \cdot \left( 4y^2+24y+36\right) = 80y^3+480y^2+720y-64y^4-384y^3-576y^2 $$ |
| ④ | Combine like terms: $$ \color{blue}{80y^3} + \color{red}{480y^2} +720y-64y^4 \color{blue}{-384y^3} \color{red}{-576y^2} = -64y^4 \color{blue}{-304y^3} \color{red}{-96y^2} +720y $$ |
This page was created using
Simplify polynomials calculator